Hmm. I worked in a little mom and pop one hour lab in 1990, and they had an older machine of the sort which was pretty standard in most of the places I saw around at the time. It wasn't much like anything described here so far, I'd say.
We used standard Fuji or Agfa machines, as did many others. You fed the film into one machine, and got dry negs out the other end ten or fifteen minutes later. The printing (4x6 was as common as 3.5x5) was all done with rolled paper
which was put into a cassette in the dark, then loaded into the print machine.
The negatives (all still in a roll) were fed through a little window one at a time, and you would guess about the adjustment, with a few simple controls- more denisty or less, basically- and push a button. The exposure was made, and you feed the roll to the next frame, then do it again. The film was hung up on a rack, and when the prints came out a few minutes later, you went through them to make sure they looked ok. If so, the negatives were cut and sleeved, and the whole thing was packaged into those envelopes we all remember. If the prints looked really bad, you did it over till they looked right- and if it took you more than two prints to get it to look ok, the boss would get mad, because the time and expense would eat into the (slim) profit.
Have you seen the movie "Hope Floats"? The main character gets a job at a little local mini-lab, and she struggles with just such a machine. There's a scene where the boss gives her a simplified/Hollywood training on the thing, and while it's not exactly accurate, it gives you an idea of the process, plus a reasonable look at the sort of machine that I would say was the most common way of making prints in that era. It's not a great movie, but probably worth seeing for your research.
Let us know what you come up with!